Raw data quality control
Initialization
We start the analysis by initializing the packages required for all the analysis performed in this section. We also define the root directory, within which all the input/output operations for this project will be performed. At the end of this document, detailed software version information is provided for easier reproducibility of the analysis.
library(reshape2)
library(ggplot2)
library(ggrepel)
library(ggpubr)
library(lsr)
library(plotly)
library(DT)
library(WriteXLS)
library(ggallin)
path = "/Users/ashwin/Documents/Projects/YeastScreen/Essential_DAmP_screen/"Cleaning raw data
Firstly we read the raw yeast redox screen data and remove outlier (extreme values) and NA. Typically, outlier removal is not considered good data analysis practice, however, we do it here because we know that the extreme values comes from technical artifacts. For example, roGFP2 ratios cannot be negative and those which are significantly higher than the plate average are ambiguous signals.
Outliers were detected as -
- upper outlier values > 75th quantile value for a plate + 3 * plate IQR value
- lower outlier values < 25th quantile value for a plate - 3 * plate IQR value
The outlier values are all set to NA and values greater than the lower bound threshold but less than 0 were set to pseudo minimum value of 0.0001 as roGFP2 ratios can’t be less than 0.
We show these extreme outliers below, ploting the distribution of values from each plate.
rawDat = readRDS(paste0(path, "data/workspaces/YeastMutantRedox_RawData.RDS"))
tmpdat = na.omit(rawDat)
ggplot(tmpdat, aes(x = roGFP2.ratio, color = Plate)) + geom_density() + theme_bw(base_size = 8) +
labs(x = "roGFP2 ratio (in log10)") + scale_x_continuous(trans = pseudolog10_trans,
breaks = c(-50, -2:5, 50)) + facet_wrap(Content ~ Type, scales = "free") + theme(legend.position = "none",
panel.grid = element_blank())
rawDat = readRDS(paste0(path, "data/workspaces/YeastMutantRedox_RawData.RDS"))
rawDatCleaned = vector("list", length = 3)
names(rawDatCleaned) = c("Glucose", "Galactose", "Glycerol")
for (i in names(rawDatCleaned)) {
dat = rawDat[rawDat$Type == i, ]
dat = split(dat, dat$Plate)
dat = lapply(dat, function(x) {
vals = x$roGFP2.ratio
lb = quantile(vals, probs = 0.25, na.rm = T) - (3 * IQR(vals, na.rm = T))
ub = quantile(vals, probs = 0.75, na.rm = T) + (3 * IQR(vals, na.rm = T))
vals[vals < lb | vals > ub] = NA
vals[vals > lb & vals < 0] = 10^-4
x$roGFP2.ratio = vals
x = x[!is.na(x$roGFP2.ratio), ]
return(x)
})
rawDatCleaned[[i]] = do.call("rbind", dat)
rm(dat)
}
rawDatCleaned = do.call("rbind", rawDatCleaned)
rawDatCleaned = droplevels(rawDatCleaned)
rownames(rawDatCleaned) = 1:nrow(rawDatCleaned)Next, lets check the summaries of the raw roGFP2 redox screen data and the cleaned raw data for comparison.
Raw data looked like -
Plate Well_96 Well Group
2 : 3888 A11 : 576 A41 : 36 AL : 576
4 : 3840 D10 : 576 A42 : 36 AT : 576
3 : 3792 D2 : 576 A43 : 36 K : 576
9 : 3696 A1 : 528 A44 : 36 A : 528
8 : 3360 D1 : 528 B41 : 36 AK : 528
5 : 3216 D5 : 528 B42 : 36 AO : 528
(Other):16032 (Other):34512 (Other):37608 (Other):34512
Content SystematicName SGD.ID Gene.Symbol
Blank :9456 Length:37824 Length:37824 Length:37824
Control :9456 Class :character Class :character Class :character
Cytoplasm :9456 Mode :character Mode :character Mode :character
Mitochondria:9456
roGFP2.ratio Type
Min. :-9.746 Glucose :12608
1st Qu.: 0.469 Galactose:12608
Median : 0.568 Glycerol :12608
Mean : 0.648
3rd Qu.: 0.817
Max. : 6.500
NA's :9456 Cleaned data looked like -
Plate Well_96 Well Group
2 : 2902 A11 : 432 A41 : 36 AT : 432
4 : 2862 D10 : 432 A42 : 36 K : 432
3 : 2822 D2 : 428 A43 : 36 AL : 428
9 : 2771 D5 : 396 A44 : 36 AO : 396
8 : 2520 D7 : 396 B41 : 36 AQ : 396
5 : 2412 E6 : 396 B42 : 36 BB : 396
(Other):12004 (Other):25813 (Other):28077 (Other):25813
Content SystematicName SGD.ID Gene.Symbol
Control :9427 Length:28293 Length:28293 Length:28293
Cytoplasm :9437 Class :character Class :character Class :character
Mitochondria:9429 Mode :character Mode :character Mode :character
roGFP2.ratio Type
Min. :0.0001 Glucose :9428
1st Qu.:0.4692 Galactose:9431
Median :0.5678 Glycerol :9434
Mean :0.6447
3rd Qu.:0.8155
Max. :2.1274
Below is the table of cleaned raw data, which will be used in all of the next analyses
datatable(rawDatCleaned, rownames = FALSE, filter = "top", class = "compact", extensions = c("Buttons"),
options = list(autoWidth = TRUE, dom = "Blfrtip", buttons = c("csv", "excel",
"print")))Distribution of raw roGFP2 ratios
Distribution of raw roGFP2 ratios (absolute ratios) per plate
ggplot(rawDatCleaned) + theme_bw(base_size = 9) + geom_boxplot(aes(x = Plate, y = roGFP2.ratio),
outlier.size = 0.1) + facet_grid(Content ~ Type, scales = "free") + theme(axis.text.x = element_text(angle = 90,
hjust = 0.5, vjust = 0.5))
Identification of edge effects
A well known technical issue with yeast mutant screens is the altered growth characteristics of yeast colonies growing at the edge of plates. Next, we look at how roGFP2 ratios are different between edge wells and non-edge wells.
These are the edge wells and the mutants originating from these locations should be carefully analyzed.
# edge = unique(c( paste0(c(LETTERS, letters[1:6]), '01'), #left
# paste0(c(LETTERS, letters[1:6]), '48'), #right paste0('A', c(paste0(0,1:9),
# 10:48)), #top paste0('f', c(paste0(0,1:9), 10:48)) #bottom ))
edge = as.character(unlist(read.csv(paste0(path, "data/annotations/edge_wells.txt"))))
# Print edge wells
edge [1] "I01" "Q01" "Y01" "A03" "D02" "F04" "I03" "L02" "N04" "Q03" "T02" "V04"
[13] "Y03" "b02" "d04" "A09" "A17" "A25" "A33" "A41" "B05" "B13" "B21" "B29"
[25] "B37" "B45" "C09" "C17" "C25" "C33" "C41" "D05" "D13" "D21" "D29" "D37"
[37] "D45" "F45" "H45" "J45" "L45" "N45" "P45" "R45" "T45" "V45" "X45" "Z45"
[49] "b05" "b13" "b21" "b29" "b37" "b45" "c09" "c17" "c25" "c33" "c41" "d05"
[61] "d13" "d21" "d29" "d37" "d45" "e09" "e17" "e25" "e33" "e41" "J01" "R01"
[73] "Z01" "A04" "D03" "G02" "I04" "L03" "O02" "Q04" "T03" "W02" "Y04" "b03"
[85] "e02" "A10" "A18" "A26" "A34" "A42" "B06" "B14" "B22" "B30" "B38" "B46"
[97] "C10" "C18" "C26" "C34" "C42" "D06" "D14" "D22" "D30" "D38" "D46" "F46"
[109] "H46" "J46" "L46" "N46" "P46" "R46" "T46" "V46" "X46" "Z46" "b06" "b14"
[121] "b22" "b30" "b38" "b46" "c10" "c18" "c26" "c34" "c42" "d06" "d14" "d22"
[133] "d30" "d38" "d46" "e10" "e18" "e26" "e34" "e42" "K01" "S01" "a01" "B02"
[145] "D04" "G03" "J02" "L04" "O03" "R02" "T04" "W03" "Z02" "b04" "e03" "A11"
[157] "A19" "A27" "A35" "A43" "B07" "B15" "B23" "B31" "B39" "B47" "C11" "C19"
[169] "C27" "C35" "C43" "D07" "D15" "D23" "D31" "D39" "D47" "F47" "H47" "J47"
[181] "L47" "N47" "P47" "R47" "T47" "V47" "X47" "Z47" "b07" "b15" "b23" "b31"
[193] "b39" "b47" "c11" "c19" "c27" "c35" "c43" "d07" "d15" "d23" "d31" "d39"
[205] "d47" "e11" "e19" "e27" "e35" "e43" "L01" "T01" "b01" "B03" "E02" "G04"
[217] "J03" "M02" "O04" "R03" "U02" "W04" "Z03" "c02" "e04" "A12" "A20" "A28"
[229] "A36" "A44" "B08" "B16" "B24" "B32" "B40" "B48" "C12" "C20" "C28" "C36"
[241] "C44" "D08" "D16" "D24" "D32" "D40" "D48" "F48" "H48" "J48" "L48" "N48"
[253] "P48" "R48" "T48" "V48" "X48" "Z48" "b08" "b16" "b24" "b32" "b40" "b48"
[265] "c12" "c20" "c28" "c36" "c44" "d08" "d16" "d24" "d32" "d40" "d48" "e12"
[277] "e20" "e28" "e36" "e44" "M01" "U01" "c01" "B04" "E03" "H02" "J04" "M03"
[289] "P02" "R04" "U03" "X02" "Z04" "c03" "A05" "A13" "A21" "A29" "A37" "A45"
[301] "B09" "B17" "B25" "B33" "B41" "C05" "C13" "C21" "C29" "C37" "C45" "D09"
[313] "D17" "D25" "D33" "D41" "E45" "G45" "I45" "K45" "M45" "O45" "Q45" "S45"
[325] "U45" "W45" "Y45" "a45" "b09" "b17" "b25" "b33" "b41" "c05" "c13" "c21"
[337] "c29" "c37" "c45" "d09" "d17" "d25" "d33" "d41" "e05" "e13" "e21" "e29"
[349] "e37" "e45" "N01" "V01" "d01" "C02" "E04" "H03" "K02" "M04" "P03" "S02"
[361] "U04" "X03" "a02" "c04" "A06" "A14" "A22" "A30" "A38" "A46" "B10" "B18"
[373] "B26" "B34" "B42" "C06" "C14" "C22" "C30" "C38" "C46" "D10" "D18" "D26"
[385] "D34" "D42" "E46" "G46" "I46" "K46" "M46" "O46" "Q46" "S46" "U46" "W46"
[397] "Y46" "a46" "b10" "b18" "b26" "b34" "b42" "c06" "c14" "c22" "c30" "c38"
[409] "c46" "d10" "d18" "d26" "d34" "d42" "e06" "e14" "e22" "e30" "e38" "e46"
[421] "O01" "W01" "e01" "C03" "F02" "H04" "K03" "N02" "P04" "S03" "V02" "X04"
[433] "a03" "d02" "A07" "A15" "A23" "A31" "A39" "A47" "B11" "B19" "B27" "B35"
[445] "B43" "C07" "C15" "C23" "C31" "C39" "C47" "D11" "D19" "D27" "D35" "D43"
[457] "D47" "G47" "I47" "K47" "M47" "O47" "Q47" "S47" "U47" "W47" "Y47" "a47"
[469] "b11" "b19" "b27" "b35" "b43" "c07" "c15" "c23" "c31" "c39" "c47" "d11"
[481] "d19" "d27" "d35" "d43" "e07" "e15" "e23" "e31" "e39" "e47" "P01" "X01"
[493] "A02" "C04" "F03" "I02" "K04" "N03" "Q02" "S04" "V03" "Y02" "a04" "d03"
[505] "A08" "A16" "A24" "A32" "A40" "A48" "B12" "B20" "B28" "B36" "B44" "C08"
[517] "C16" "C24" "C32" "C40" "C48" "D12" "D20" "D28" "D36" "D44" "D48" "G48"
[529] "I48" "K48" "M48" "O48" "Q48" "S48" "U48" "W48" "Y48" "a48" "b12" "b20"
[541] "b28" "b36" "b44" "c08" "c16" "c24" "c32" "c40" "c48" "d12" "d20" "d28"
[553] "d36" "d44" "e08" "e16" "e24" "e32" "e40" "e48"edgeDat = rep("non edge wells", nrow(rawDatCleaned))
edgeDat[rawDatCleaned$Well %in% edge] = "edge wells"
edge = rawDatCleaned
edge$edge = edgeDat
rm(edgeDat)Visulaizing the differences using both effect size (Fold change, Cohen D) and pvalue
# Computing distribution difference statistics
stats = split(edge, paste(edge$Plate, edge$Type, edge$Content, sep = "-"))
stats = t(sapply(stats, function(x) {
y = x$roGFP2.ratio[x$edge == "edge wells"]
n = x$roGFP2.ratio[x$edge == "non edge wells"]
fc = log2(median(y, na.rm = T)/median(n, na.rm = T))
pv = wilcox.test(y, n)$p.value
# cd = effectsize::cohens_d(y, n, pooled_sd = F)$Cohens_d p = signif(p,2)
# return(c(log2fc = fc, wilcoxP = pv, CohenD = cd))
return(c(log2fc = fc, wilcoxP = pv))
}))
a = do.call("rbind", strsplit(rownames(stats), "-"))
colnames(a) = c("Plate", "Nutrient", "Condition")
stats = data.frame(a, stats, row.names = NULL, stringsAsFactors = F)
stats$log2fc = round(stats$log2fc, 2)
stats$wilcoxP = signif(-log10(p.adjust(stats$wilcoxP, method = "fdr")), 2)
# stats$CohenD = round(stats$CohenD, 2)
# Volcano plot
p3 = ggplot(stats, aes(x = log2fc, y = wilcoxP, text = Plate)) + theme_bw(base_size = 8) +
xlim(-1, 1) + labs(y = "-log10(fdr pval)") + geom_point(size = 0.8) + geom_hline(yintercept = -log10(0.05)) +
geom_vline(xintercept = c(-0.5, 0.5), lty = 2) + geom_vline(xintercept = c(-1,
1), lty = 1) + facet_wrap(Nutrient ~ Condition, scales = "free") + geom_text_repel(data = stats[abs(stats$log2fc) >
0.5 & stats$wilcoxP > -log10(0.05), ], aes(label = Plate), size = 2) + theme(panel.grid = element_blank())
ggsave(filename = paste0(path, "analysis/QC/roGFP2_ratio_RAWdata_edge_effects_badPlates.pdf"),
plot = p3, width = 7.5, height = 6)
ggplotly(p3)Variance among controls
Next we look into the variance exhibited by the controls across plates and nutrient conditions. Ideally, all controls in the plate should have similar values i.e variance close to zero. Below we show the variance of raw roGFP2 ratios among controls per plate and group.
ctrlVar = rawDatCleaned %>% filter(Content == "Control") %>% select(Gene.Symbol,
Plate, Type, Group, roGFP2.ratio) %>% group_by(Plate, Type, Group) %>% mutate(Control_variance = round(var(roGFP2.ratio,
na.rm = T), 4)) %>% ungroup() %>% select(Gene.Symbol, Plate, Type, Group, Control_variance) %>%
rename(Genes = Gene.Symbol, Nutrient = Type) %>% mutate(Plate = paste0("P-",
Plate)) %>% distinct()
plot_ly(ctrlVar, x = ~Group, y = ~Plate, z = ~Control_variance, text = ~Genes, type = "scatter3d",
mode = "markers", marker = list(size = 3), opacity = 1, color = ~Nutrient)Next we remove all genes with variance among controls > 0.05
rmv = ctrlVar[which(ctrlVar$Control_variance > 0.05), ]
rmv$Plate = gsub("P-", "", rmv$Plate)
rmv = paste(rmv$Genes, rmv$Plate, rmv$Nutrient, sep = "-")
paste0("Number of poor control genes removed - ", length(rmv))[1] "Number of poor control genes removed - 12"matchID = paste(rawDatCleaned$Gene.Symbol, rawDatCleaned$Plate, rawDatCleaned$Type,
sep = "-")
rawDatCleaned_ctrlfilt = rawDatCleaned[!matchID %in% rmv, ]
ctrlVar = rawDatCleaned_ctrlfilt %>% filter(Content == "Control") %>% select(Gene.Symbol,
Plate, Type, Group, roGFP2.ratio) %>% group_by(Plate, Type, Group) %>% mutate(Control_variance = round(var(roGFP2.ratio,
na.rm = T), 4)) %>% ungroup() %>% select(Gene.Symbol, Plate, Type, Group, Control_variance) %>%
rename(Genes = Gene.Symbol, Nutrient = Type) %>% mutate(Plate = paste0("P-",
Plate)) %>% distinct()
plot_ly(ctrlVar, x = ~Group, y = ~Plate, z = ~Control_variance, text = ~Genes, type = "scatter3d",
mode = "markers", marker = list(size = 3), opacity = 1, color = ~Nutrient)Next we we visualize the fact that in a good screen, individual control values should not deviate much from the median value of all controls from that same plate. For a given plate \(i\), the normalized control values i.e \(NormCtrl\) is given as - \[NormCtrl_i = \frac{Ctrl_i} {median(Ctrl_i)}\] We plot these scaled control values per plate across conditions below. Ideally these values should be close to 1 (shown as red horizontal lines). A table for these scaled control values is also provided.
ctrlDat = split(rawDatCleaned_ctrlfilt, rawDatCleaned_ctrlfilt$Type)
ctrlDat = lapply(ctrlDat, function(x) {
split(x, x$Plate)
})
for (i in 1:length(ctrlDat)) {
for (j in 1:length(ctrlDat[[i]])) {
tmp = droplevels(ctrlDat[[i]][[j]])
tmp = tmp[, -2]
# Plate control
tmp.ctrl = tmp[tmp$Content == "Control", ]
# Normalizing factor
nf = median(tmp.ctrl$roGFP2.ratio, na.rm = T)
# Measure control value deviation from plate median
ctrlDat[[i]][[j]] = data.frame(Gene = tmp.ctrl$Gene.Symbol, NormControl = round(tmp.ctrl$roGFP2.ratio/nf,
3), stringsAsFactors = F)
# Deleting
rm(tmp, tmp.ctrl, nf)
}
rm(j)
}
rm(i)
ctrlDat = melt(ctrlDat, id = "Gene")
ctrlDat = ctrlDat[, c(4, 5, 1, 3)]
colnames(ctrlDat) = c("Plate", "Nutrient", "Gene", "NormControl")
ctrlDat$Plate = as.factor(ctrlDat$Plate)
ctrlDat$Nutrient = factor(ctrlDat$Nutrient, levels = c("Glucose", "Galactose", "Glycerol"))
datatable(ctrlDat, rownames = FALSE, filter = "top", class = "compact", extensions = c("Buttons"),
options = list(autoWidth = TRUE, dom = "Blfrtip", buttons = c("csv", "excel")))ggplot(ctrlDat) + theme_bw(base_size = 8) + labs(y = "Control / Median plate control (roGFP2 ratios)") +
geom_boxplot(aes(x = Plate, y = NormControl), outlier.size = 0.1, lwd = 0.2) +
facet_wrap(~Nutrient) + geom_hline(yintercept = 1, color = "grey80") + geom_hline(yintercept = 2,
color = "black") + geom_text_repel(data = subset(ctrlDat, NormControl > 3), aes(x = Plate,
y = NormControl, label = Gene), size = 2) + theme(axis.text.x = element_text(angle = 90,
hjust = 0.5, vjust = 0.5))
Next we remove those controls that deviate a lot from 1
rmv = ctrlDat[which(ctrlDat$NormControl > 2), ]
rmv = paste(rmv$Gene, rmv$Plate, rmv$Nutrient, sep = "-")
ctrlDat = ctrlDat[which(ctrlDat$NormControl < 2), ]
paste0("Number of control genes removed which deviated (>2) from the plat median - ",
nrow(rmv))[1] "Number of control genes removed which deviated (>2) from the plat median - "matchID = paste(rawDatCleaned_ctrlfilt$Gene.Symbol, rawDatCleaned_ctrlfilt$Plate,
rawDatCleaned_ctrlfilt$Type, sep = "-")
rawDatCleaned_ctrlfilt = rawDatCleaned_ctrlfilt[!matchID %in% rmv, ]Plotting these scaled control values -
p = ggplot(ctrlDat) + theme_bw(base_size = 8) + labs(y = "Control / Median plate control (roGFP2 ratios)") +
geom_boxplot(aes(x = Plate, y = NormControl), outlier.size = 0.1, lwd = 0.2) +
facet_wrap(~Nutrient) + geom_hline(yintercept = 1, color = "red") + geom_text_repel(data = subset(ctrlDat,
NormControl > 3), aes(x = Plate, y = NormControl, label = Gene), size = 2) +
theme(axis.text.x = element_text(angle = 90, hjust = 0.5, vjust = 0.5))
ggsave(filename = paste0(path, "analysis/QC/roGFP2_ratio_RAWdata_Controls_normalized_by_plate_control_median.pdf"),
plot = p, width = 20, height = 7)
p
A more standard way of calculating the variance among the controls is by computing the robust coefficient of variance see here. For a given plate \(i\), this is given as - \[CoefVar_i = \frac{mad(Ctrl_i)}{median(Ctrl_i)}\] mad is Median absolute deviation
Plotting these robust coefficient of variation for control values-
cvDat = split(ctrlDat, ctrlDat$Nutrient)
cvDat = lapply(cvDat, function(x) {
a = split(x, x$Plate)
b = lapply(a, function(y) mad(y$NormControl)/median(y$NormControl))
return(b)
})
cvDat = melt(cvDat)
cvDat = cvDat[, c(2, 3, 1)]
colnames(cvDat) = c("Plate", "Nutrient", "Dev")
cvDat$Plate = as.factor(cvDat$Plate)
cvDat$Nutrient = factor(cvDat$Nutrient, levels = c("Glucose", "Galactose", "Glycerol"))
p = ggplot(cvDat, aes(Plate, Dev)) + theme_bw(base_size = 8) + labs(y = "% of deviation from median plate control roGFP2 ratios") +
geom_bar(stat = "identity") + facet_wrap(~Nutrient) + geom_hline(yintercept = 0.5,
color = "black") + geom_hline(yintercept = 1, color = "red") + theme(panel.grid = element_blank(),
axis.text.x = element_text(angle = 90, hjust = 0.5, vjust = 0.5))
ggsave(filename = paste0(path, "analysis/QC/roGFP2_ratio_RAWdata_Controls_Coef_variation.pdf"),
plot = p, width = 12, height = 3.5)
p
Since plate 150 in Glucose clearly seems to be an extreme outlier we remove it from further analysis
rawDatCleaned_ctrlfilt = rawDatCleaned_ctrlfilt[!(rawDatCleaned_ctrlfilt$Type ==
"Glucose" & rawDatCleaned_ctrlfilt$Plate == 150), ]Saving the data
Finally we save the cleaned raw Data as a .RDS (R data object), which will be used for the next step of normalization
Session information
R version 3.6.2 (2019-12-12)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS 10.16
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRlapack.dylib
locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] ggallin_0.1.1 WriteXLS_5.0.0 DT_0.12 plotly_4.9.2
[5] lsr_0.5 ggpubr_0.2.4 magrittr_1.5 ggrepel_0.8.1
[9] ggplot2_3.2.1 reshape2_1.4.3 rmdformats_0.3.6 knitr_1.28
loaded via a namespace (and not attached):
[1] tidyselect_1.0.0 xfun_0.12 purrr_0.3.3 colorspace_1.4-1
[5] vctrs_0.2.2 htmltools_0.4.0 viridisLite_0.3.0 yaml_2.2.1
[9] rlang_0.4.4 pillar_1.4.3 later_1.0.0 glue_1.3.1
[13] withr_2.1.2 RColorBrewer_1.1-2 lifecycle_0.1.0 plyr_1.8.5
[17] stringr_1.4.0 munsell_0.5.0 ggsignif_0.6.0 gtable_0.3.0
[21] htmlwidgets_1.5.1 evaluate_0.14 labeling_0.3 fastmap_1.0.1
[25] Cairo_1.5-11 httpuv_1.5.5 crosstalk_1.0.0 Rcpp_1.0.3
[29] xtable_1.8-4 scales_1.1.0 promises_1.1.0 formatR_1.7
[33] jsonlite_1.6.1 mime_0.9 farver_2.0.3 digest_0.6.23
[37] stringi_1.4.5 bookdown_0.17 dplyr_0.8.4 shiny_1.4.0
[41] grid_3.6.2 tools_3.6.2 lazyeval_0.2.2 tibble_2.1.3
[45] crayon_1.3.4 tidyr_1.0.2 pkgconfig_2.0.3 ellipsis_0.3.0
[49] data.table_1.12.8 assertthat_0.2.1 rmarkdown_2.1 httr_1.4.1
[53] R6_2.4.1 compiler_3.6.2